Three particles A, B and C move along the same straight line. Their masses are 1kg, 2kg and 3kg respectively. At a particular instant, constant forces of 3N, 3N and 6N act on A, B and C in the positive direction of the line.
a. (i) Derive an expression for the acceleration of each particle in terms of the given data without substituting numerical values.
b. (ii) Using your expressions, rank the three accelerations from greatest to least, showing your reasoning.
c. (iii) Suppose both the force and the mass of particle C are simultaneously doubled. Prove that its acceleration remains unchanged, and explain the underlying principle.